The present invention relates generally to Fourier transform holograms and more specifically the invention pertains to two pixel-oriented methods for designing Fourier transform holograms, pseudorandom encoding and minimum distance encoding.
Today the leading methods of designing Fourier transform holograms for laser pattern generation and optical interconnects use iterative search and numerical optimization procedures that vary the modulation values and various degrees of freedom to achieve acceptable diffraction patterns. In this prior work it is normally assumed that the design is to be realized as a fixed pattern diffractive optical element (DOE) that is subsequently mass-produced, which makes computation times of a few minutes to hours insignificant compared to the time required to fabricate the device. However, our previous studies on real-time programmable spatial light modulators and DOE rapid prototyping systems has led us to reconsider the design problem with particular emphasis on significantly reducing the design time.
By far, the fastest design algorithms are those that directly map a desired complex-valued function into a transmittance function that can be physically produced by the available modulator. The delayed-sampling method of Brown and Lohmann is one of the earliest applications in optics of this idea. The numerical speed of this and many other mapping/encoding methods that were evaluated in the first decade of computer generated holography is due to serial encoding of each desired complex value into a corresponding value of transmittance. Since the various degrees of freedom are not included in this design approach (e.g. in the design of most spot array generators where the phase of the far-field diffraction pattern is usually not of concern), the performance of the encoding method in terms of diffraction efficiency or other related metrics can be substantially less than for the optimization methods. Nonetheless, we believe there are applications that would benefit from the faster encoding algorithms.